Just one question: do you want/need babies?
If not- chuck the nestbox!
EXACTLY!!!! Christa nailed your problem spot-on!
The reason your birds are acting the way that they are is because their hormones are raging. And the reason their hormones are raging is because you have a nest-box in their cage...Nest-boxes are not meant to be cage decorations or to be used on a regular basis, and should not be used EVER unless you are purposely trying to breed your birds. That's what they are for. Otherwise, they are of no use to you at all, and they will only serve to cause you grief and can actually result in severe injury or death of one or both of your birds. As it is now they aren't really safe being together, as the male could very well hurt the female badly the way things are going...
You should not have ANY small, dark places for your birds to get inside of or underneath inside of their cage, such as nest-boxes, beds (like the triangle-beds they sell for them), no tents, no "Happy/Snuggle Huts", no hammocks, no other types of boxes of any kind, and absolutely nothing that can be used as "nesting-material" in the bottom of the cage, like any type of animal bedding, wood-chips, shredded paper or Carefresh bedding, no shredded newspaper, etc. There should only be newspaper sheets or some other type of cage-liners in the very bottom of their cage underneath the grate so they cannot get to it and start shredding it up to use as nesting material...They don't need anything to sleep on/in except for their perches, and they don't ever need any type of "nest" at all unless you're trying to breed them...
Same goes for when they are outside of their cage in your home, they shouldn't be allowed to get underneath of furniture, behind pillows on the couch, underneath blankets/towels, etc. All of these things will cause their hormones to rage, and sometimes it can happen instantaneously, for example if one of them goes under the couch or behind a pillow for a minute or two, they can literally come back out in a kind of "hormonal Trance" where they are extremely aggressive and violent with not only other birds but with people as well...
So you need to remove the nest-box ASAP, and over the next week or so you should see their behavior towards each other settle-down and the aggression and fighting should stop.
I don't know if you're purposely trying to breed them, but if you have no experience doing so and have no hand-raising/hand-feeding experience, nor any of the necessary equipment such as a Brooder, a cooking/candy thermometer, oral syringes, formula, etc., and you've never been mentored in how to care for baby birds who are not weaned then it's a really bad idea to breed them, because chances are, based on the behavior you are describing so far, that they are not going to make very good parents, and even if it's not your plan you may very well end-up having to pull the babies from the nest-box very early and hand-raise/hand-feed them yourself due to aggression from one or both of them.
